no. 19-20
Complex analysis/Functional analysis
Weighted-composition operators on Np-spaces in the ball
Presented by: Jean-Pierre Demailly
Hu, Bingyang1; Khoi, Le Hai1
1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore
Comptes Rendus. Mathématique, Volume 351 (2013) no. 19-20, pp. 719-723

In this Note, we introduce Np-spaces, some kind of Bergman-type spaces, of holomorphic functions in the unit ball of Cn. Basic properties of these spaces are provided. We study weighted-composition operators between Np-spaces and the spaces A−q and obtain, in particular, criteria for boundedness and compactness of such operators.

Dans cette Note, nous introduisons les espaces Np, qui sont des analogues dʼespaces de Bergman de fonctions holomorphes sur la boule unité de Cn. Les propriétés de base de ces espaces sont données. Nous étudions ensuite les opérateurs de composition à poids de Np dans A−q, et nous obtenons, en particulier, des critères pour que ces opérateurs soient bornés ou compacts.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.10.002

Hu, Bingyang 1; Khoi, Le Hai 1

1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore 
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Hu, Bingyang; Khoi, Le Hai. Weighted-composition operators on $ {\mathcal{N}}_{p}$-spaces in the ball. Comptes Rendus. Mathématique, Volume 351 (2013) no. 19-20, pp. 719-723. doi: 10.1016/j.crma.2013.10.002

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[6] Shapiro, J.H. Compositions Operators and Classical Function Theory, Springer-Verlag, New York, 1993

[7] Ueki, S. Weighted composition operators acting between the Np-space and the weighted-type space Hα∞, Indag. Math., Volume 23 (2012), pp. 243-255

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